Problem: Simplify the following expression: $n = \dfrac{-7r + 49}{42r + 42}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-7r + 49 = - (7 \cdot r) + (7\cdot7)$ The denominator can be factored: $42r + 42 = (2\cdot3\cdot7 \cdot r) + (2\cdot3\cdot7)$ The greatest common factor of all the terms is $7$ Factoring out $7$ gives us: $n = \dfrac{(7)(-r + 7)}{(7)(6r + 6)}$ Dividing both the numerator and denominator by $7$ gives: $n = \dfrac{-r + 7}{6r + 6}$